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The Effects of Variable Thermal Conductivity in Thermoelastic Interactions in an Infinite Material with and without Kirchhoff’s Transformation

Author

Listed:
  • Aatef Hobiny

    (Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 22254, Saudi Arabia)

  • Ibrahim Abbas

    (Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 22254, Saudi Arabia
    Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt)

Abstract

In this paper, the problem of an unbonded material under variable thermal conductivity with and without Kirchhoff’s transformations is investigated. The context of the problem is the generalized thermoelasticity model. The boundary plane of the medium is exposed to a thermal shock that is time-dependent and considered to be traction-free. Because nonlinear formulations are difficult, the finite element method is applied to solve the problem without Kirchhoff’s transformations. In a linear case, when using Kirchhoff’s transformations, the problem’s solution is derived using the Laplace transforms and the eigenvalue approach. The effect of variable thermal conductivity is discussed and compared with and without Kirchhoff’s transformations. The graphical representations of numerical results are shown for the distributions of temperature, displacement and stress.

Suggested Citation

  • Aatef Hobiny & Ibrahim Abbas, 2022. "The Effects of Variable Thermal Conductivity in Thermoelastic Interactions in an Infinite Material with and without Kirchhoff’s Transformation," Mathematics, MDPI, vol. 10(22), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4176-:d:966452
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    References listed on IDEAS

    as
    1. Faris Alzahrani, 2020. "The Effects of Variable Thermal Conductivity in Semiconductor Materials Photogenerated by a Focused Thermal Shock," Mathematics, MDPI, vol. 8(8), pages 1-9, July.
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    Cited by:

    1. A. V. Sedelnikov & D. I. Orlov & V. V. Serdakova & A. S. Nikolaeva, 2023. "Investigation of the Stress-Strain State of a Rectangular Plate after a Temperature Shock," Mathematics, MDPI, vol. 11(3), pages 1-12, January.

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